R. Verma - Department of Management Control and Information Systems, University of Chile, Av. Diagonal Paraguay ۲۵۷, ۸۳۳۰۰۱۵ Santiago, Chile
A. Aggarwal - University School of Basic and Applied Sciences\ Guru Gobind Singh Indraprastha University Delhi-۱۱۰۰۷۸, India

In real-world decision-making problems, experts often prefer to express their views, regarding problem parameters, in a natural language rather than precise numerical form. Linguistic representation models have been widely used to solve many decision-making problems with qualitative information. Game theory has been found successful applications in a wide range of areas. This paper presents an extensive study of matrix games with qualitative payoffs. The work uses ۲-tuple intuitionistic fuzzy linguistic values (۲-TIFLVs) to represent the payoffs of the matrix game. We develop the mathematical formulation and concepts of the solutions for matrix games with payoffs represented by ۲-TIFLVs. Paper also shows that matrix games with payoffs of ۲-TIFLVs have solutions that can be obtained by transforming the matrix game in a pair of linear/nonlinear programming problems. Finally, a real-life numerical is given to illustrate the developed method.

Matrix game, linguistic variables, ۲-tuple linguistic model, ۲-tuple intuitionistic fuzzy linguistic set, non-linear optimization